An exact solution for stresses and displacements of pressurized FGM thick-walled spherical shells with exponential-varying properties

Nejad, Mohammad Zamani; Abedi, Majid; Lotfian, Mohammad Hassan; Ghannad, Mehdi

doi:10.1007/s12206-012-0908-3

Cited by 21 publications

(13 citation statements)

References 10 publications

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“…(12) The only nontrivial equilibrium equation is [5], (13) Similarly, according to stress equilibrium equations, the governing equation of displacement becomes (14) with boundary conditions that come from radial stress, (15) where obtained as below depends on the r. Subscript s represents spherical vessel.…”

Section: Basic Formulation Of Spherical Pressure Vesselmentioning

confidence: 99%

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The Effect of the Poisson Ratio on Stresses of Heterogeneous Pressure Vessels

Eker

Yarımpabuç²,

Çelebi³

2018

European Mechanical Science

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Functionally graded materials (FGM) belong to advanced composite materials class whose mechanical properties vary continuously from one surface to another at macro level. Thick walled annular structures are widely used in industry as nuclear reactors, long pipes used for carrying gases/oil, pressure vessels etc. Elastic analysis of FG thick walled cylindrical and spherical pressure vessels subjected only to internal pressure are studied. The material properties (Young' s modulus-Poisson' s ratio) are assumed to obey the power-law function through the wall thickness. Under these assumptions the governing equations of the FG vessels become a two-point boundary value problem. The analytical solution of such an equation can not be obtained except for simple grading functions. Complementary Functions Method is performed to solve governing equation in order to obtain displacement and stress distributions depending on inhomogeneity parameters.

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Section: Basic Formulation Of Spherical Pressure Vesselmentioning

confidence: 99%

“…It was assumed that the volume fractions of two phases of a FGM vary only with the radius. A few more studies can be found in the literature [15,18] where different varying functions and solution procedures have been used.…”

Section: Introductionmentioning

confidence: 99%

The Effect of the Poisson Ratio on Stresses of Heterogeneous Pressure Vessels

Eker

Yarımpabuç²,

Çelebi³

2018

European Mechanical Science

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“…Analytical studies have been performed in recent years [1–4]. Also numerical studies have been performed [5–26]. Function types to be used for grading of isotropic or anisotropic behavior for pressurized hollow structures are very diverse.…”

Section: Introductionmentioning

confidence: 99%

“…Closed form solutions are obtained for the power rule [5, 6, 9, 11, 12, 18, 20, 22, 24, 27]. The exponential grading rule also gives exact solutions [7, 15–17, 19–21, 24–26]. The linear functions lead to analytical solution [19].…”

Section: Introductionmentioning

confidence: 99%

Exact elasticity solutions to rotating pressurized axisymmetric vessels made of functionally graded materials (FGM)

Kaçar

2020

Materialwissenschaft Werkst

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In this study the plane elasticity equations of pressurized and rotating structures, generalized analytical closed-form solutions are presented for hollow cylinders, spheres and thin disks. Three well known material pairs are graded in radial direction by using the power rule for various boundary and load conditions. Stress and displacement solutions are obtained. The effect of a constant rotational velocity is also investigated separately in absence of the internal and external pressures. Crucial results are also presented in tabular form. Keywords: Functionally graded material / elastic analysis / power rule / pressurized vessel / stress and displacement In dieser Studie werden die ebenen Elastizitätsgleichungen von unter Druck stehenden dickwandigen rotierenden zylindrischen und kugelförmigen Gefäßen und dünnen Scheiben analytisch gelöst. Der funktional gradierte Werkstoff wird in radialer Richtung gradiert und die Einstufung variiert gemäß der Machtregel. Geschlossene Lösungen, sowohl der Radial-, als auch der Umfangsspannungen und der Radialverschiebungen, werden in der für Wissenschaftler, Designer und Ingenieure am besten geeigneten Form erhalten. Unter Berücksichtigung von drei verschiedenen Metall-Keramik-Paaren und zwei verschiedenen Randbedingungen werden die Ergebnisse der Lösungen in geschlossener Form für die rotierende Struktur grafisch dargestellt, während, sowohl der innere, als auch der äußere Druck, gleichzeitig angewendet werden. Der Effekt einer konstanten Rotationsgeschwindigkeit wird auch ohne internen und externen Druck getrennt untersucht. Entscheidende Ergebnisse werden in tabellarischer Form dargestellt.

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“…Sburlati [21] obtained an analytical solution for pressurized hollow cylinders with inner FGM coating in the framework of plane elasticity theory. Nejad et al [22] performed an analytical solution for FGM thick-walled spherical shells subjected to internal and/or external pressure, assuming an exponential law variation in material properties. Sabzikar Boroujerdy and Eslami [23] studied thermal instability of shallow spherical shells made of FGM and surface-bonded piezoelectric actuators.…”

Section: Introductionmentioning

confidence: 99%

Elastic analysis of thick-walled pressurized spherical vessels coated with functionally graded materials

2014

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In recent years, functionally graded material (FGM) has been widely explored in coating technology amongst both academic and industry communities. FGM coatings are suitable substitutes for many typical conventional coatings which are susceptible to cracking, debonding and eventual functional failure due to the mismatch of material properties at the coating/substrate interface. In this study, a thick spherical pressure vessel with an inner FGM coating subjected to internal and external hydrostatic pressure is analyzed within the context of three-dimensional elasticity theory. Young’s modulus of the coating is assumed to vary linearly or exponentially through the thickness, while Poisson’s ratio is considered as constant. A comparative numerical study of FGM versus homogeneous coating is conducted for the case of vessel under internal pressure, and the dependence of stress and displacement fields on the type of coating is examined and discussed

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An exact solution for stresses and displacements of pressurized FGM thick-walled spherical shells with exponential-varying properties

Cited by 21 publications

References 10 publications

The Effect of the Poisson Ratio on Stresses of Heterogeneous Pressure Vessels

The Effect of the Poisson Ratio on Stresses of Heterogeneous Pressure Vessels

Exact elasticity solutions to rotating pressurized axisymmetric vessels made of functionally graded materials (FGM)

Elastic analysis of thick-walled pressurized spherical vessels coated with functionally graded materials

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